It's mostly a PVP game, there are single player missions and dynamic campaigns you can play in a PVE environment, but none of those aid in researching new aircraft or upgrading the planes you are flying.
The game can be fun, but it is probably best that you stick to the lower tiers, because once you get into the higher tiers the game develops a lot of problems, mostly in mission design and balancing. For high tier aircraft, you're going to see a lot of very short games, eg. 5 minute length approximately due to the bomber rushing metagame that has developed at those tiers. It's generally not possible to stop a team that is spamming bombers from winning a match by bombing out your airfield in five minutes or less (and this is after a rules change to try to address this issue, it used to be 2 minutes or less), hence everyone does it to speed up the grind to jet aircraft. For ground forces, there are lot of issues with spawn camping, and people just sitting at the spawn sniping enemies rather than trying to capture the objectives.
The XP requirements for vehicle upgrades, which are needed to make your vehicles competitive also get prohibitively high for free players once you get to the late war and post war vehicles, practically requiring either a premium account or spending real money to outright buy the upgrades in order to get them at a reasonable pace.
Finally, there are balancing issues between vehicles, particularly in higher tiers thanks to the developer's insistence on using player statistics to determine vehicle tiering. The problem with that is it leads to a lot of undertiered American aircraft, because everyone tries to turnfight in them, which is generally not their strength. Consequently a lot of Axis vehicles are badly overtiered, in the case of the Japanese, it's due to their excellent turnfighting capabilities, and getting lots of kills on people stupid enough to turnfight a Zero. In the case of the Germans, it's due to overwhelming firepower on their late war bomber killer fighters that can do well by simply engaging enemy fighters in a head on engagement, but are otherwise not competitive against similarly tiered Allied planes.